The present invention relates to a method for manufacturing hyperbolic and hyperboloid surfaces.
Aspherical surfaces including hyperbolic and hyperboloid surfaces are very usefull for optical systems. For instance, aspherical lenses and aspherical reflecting mirrors are quite often used in order to correct an aperture aberration. However, in practice it is extremely difficult to manufacture the aspherical surfaces. It is a well known fact that it took several years to grind an aspherical reflecting mirror of a large diameter for use in an astronomical observatory. In this manner at the present it is technically as well as economically difficult to utilize the aspherical optical systems to the full extent and thus, in the optical systems such as camera lens systems various aberrations are corrected by combining a plurality of lenses. This results in that the lens systems are liable to be complicated in construction, heavy in weight and large in size.
Heretofore known methods for manufacturing the aspherical surfaces may be roughly classified into the following three methods;
(a) copy-grinding on the basis of a master curve PA0 (b) Press-molding of synthetic resin or glass material PA0 (c) cutting under numerical control with using NC machine tools.
In the methods (a) and (b) use is made of a master which has to be manufactured by skilled workers almost in a manual manner. Moreover an accuracy of the master can not be made sufficiently high. Further in the method (c) using the NC machine tools since a digital control is applied, a cut surface is inherently subjected to steps or stripes. This is particularly noticeable at a surface of large radius of curvature. In order to reduce such a drawback there has been developed an R interpolation method, but this solution could not assure the accuracy sufficiently. As described above accurate aspherical surfaces could not be manufactured by the known methods and there has not been proposed any method for easily manufacturing the aspherical surfaces having the theoretically high accuracy.